Expression of type Lambda

from the theory of proveit.statistics

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, Omega, X, x
from proveit.logic import Equals, SubsetEq
from proveit.numbers import Sum
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Lambda(X, Conditional(Equals(Prob(X), Sum(index_or_indices = [x], summand = Prob(x), domain = X)), SubsetEq(X, Omega)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

X \mapsto \left\{\textrm{Pr}\left(X\right) = \left[\sum_{x \in X}~\textrm{Pr}\left(x\right)\right] \textrm{ if } X \subseteq \Omega\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 23 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	23, 10
8	Operation	operator: 18 operand: 23
9	Operation	operator: 12 operand: 14
10	Variable
11	ExprTuple	23
12	Literal
13	ExprTuple	14
14	Lambda	parameter: 22 body: 15
15	Conditional	value: 16 condition: 17
16	Operation	operator: 18 operand: 22
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	22, 23
22	Variable
23	Variable